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THE AMEBIC AN NATURALIST [Vol. XL VI 



effect of discontinuity is lost. For some purposes the process 

 of growth might be described as continuous or gradual, and 

 for other purposes as discontinuous, for there are daily inter- 

 ruptions or variations in the rate of growth. Darwin compared 

 the evolution of species to the growth of branches on a tree. 

 Theories that would supplant Darwin's conception of continuity 

 in the evolution of species are not based on equal familiarity 

 with the facts. Constructive evolutionary progress comes by 

 gradual changes in the characters of species, not by saltatory 

 transformations of one species into another. That albinism and 

 other defects appear as mutations and show Mendelian in- 

 heritance does not destroy or even conflict with the evidences of 

 continuity in the evolution of species. 



The many different applications that can be made of such 

 terms as continuity or discontinuity show how little is gained by 

 the choice of any particular statement of biological facts as a 

 basis for deduction or mathematical elaboration. That new 

 facts can be learned by syllogizing is no longer believed. Is 

 more to be gained by turning syllogisms into mathematical 

 formulae ? Even when physical analogies can be more definitely 

 drawn the biological relations of the facts seldom permit any 

 complete application of mathematical methods of thought. 



Taking evolutionary deviations into account, the recurrent life 

 cycles of organisms could be considered as spirals and this might 

 appear to bring them within the range of mathematical treat- 

 ment. Yet no regularity of form could be ascribed to such 

 spirals, for evolutionary intercalations of new characters are not 

 merely additions at the ends of definite series, but are likely to 

 intervene in any part of the life cycle. Moreover, such inter- 

 calations are made without throwing the remainder of the cycle 

 out of adjustment. 



From the historical standpoint evolution may be presented as 

 a series of transformations, but from the standpoint of heredity 

 the results must be treated as permanent and coexistent, not 

 merely as successive reactions. Each member or part of the 

 cycle must be supposed to carry the determinants or potentiali- 

 ties, the powers of reproducing every other part. And we 

 know further that these potentialities continue to be carried in 

 latent or recapitulated form, even after they have ceased to 

 come into normal expression. In other words, the biological 

 system retains latent possibilities of reversion, the maps, as it 

 were, of courses of development long since abandoned. Even 

 though the characters be considered as irreversible in the sense 

 of having permanent transmission they are subject nevertheless 



